How to properly set domain for fluid simulation?
I am not sure I understand your exact question, so let me rephrase it in my answer to be sure we are talking about the same thing.


If your problem is that it is the domain itself which 'turns into' fluid when playing/applying the simulation, then it's normal. 
From what I know looking at the inner workings of another fluid simulation algorithm, The way the fluid is simulated is by creating a grid (65*65*65, in your case), and each cell of this grid 'knows' if it contains fluid, the speed and pressure of said fluid, and sometimes its density, or 'how much' there is.
The goal of the other (blender) objects is to act in a certain way at every frame. Roughly speaking, an inflow 'fills' some cells with fluid with a given speed at each frame, while an obstacle makes sure there is no fluid inside itself, and tweaks the speed of the fluid around itself so it doesn't go inside.
However, from your screenshots, the fluid doesn't seem to be created in the right place. This also happened when I tried to run this simulation, but differently.
After messing around a little, I found out that (at least in this file), an inflow with the "volume" setting needs to have the "Export Animated Mesh" option too to behave correctly.


A similar caveat I found years ago (but might not exist anymore) is that an inflow object half-inside half-outside the domain might cause the simulation to ask for an unreasonable amount of ram (untill the PC I used was unusable, in my case)